1. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Click anywhere to advance to the streams.

2. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards. Next Stream

3. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

4. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

5. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

6. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

7. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

8. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

9. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Counting and Cardinality (K) Know number names and the count sequence Count to tell the number of objects Compare numbers Next Stream © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

10. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Number and Operations in Base Ten (K – 5) Place value understanding Develop base-ten algorithms using place value and properties of operations Computation competencies (fluency, estimation) © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

11. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Operations and Algebraic Thinking (K-5) Concrete uses and meanings of the basic operations (word problems) Mathematical meaning and formal properties of the basic operations Prepare for later work with expressions and equations in middle school © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

12. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Number and Operations Fractions (3 – 5) Enlarge concept of number beyond whole numbers, to include fractions Use understanding of the four operations to extend arithmetic to fractions Solve word problems related to the equation ax = b (a and b fractions) © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

13. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC The Number System (6 – 8) Build concepts of positive and negative numbers Work with the rational numbers as a system governed by properties of operations Begin work with irrational numbers © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

14. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Expressions and Equations (6 – 8) Treat expressions as objects to reason about (not as instructions to compute an answer) Transform expressions using properties of operations Solve linear equations Use variables and equations as techniques to solve word problems © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

15. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Algebra (9 - 12) Seeing Structure in Expressions Arithmetic with Polynomials & Rational Expressions Creating Equations Reasoning with Equations and Inequalities © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

16. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Number and Operations in Base Ten (K – 5) Place value understanding Develop base-ten algorithms using place value and properties of operations Computation competencies (fluency, estimation) Next Stream © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

17. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Number and Operations Fractions (3 – 5) Enlarge concept of number beyond whole numbers, to include fractions Use understanding of the four operations to extend arithmetic to fractions Solve word problems related to the equation ax = b (a and b fractions) © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

18. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Functions Statistics and Probability Ratios and Proportional Relationships F CC The Number System (6 – 8) Build concepts of positive and negative numbers Work with the rational numbers as a system governed by properties of operations Begin work with irrational numbers Number and Quantity © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

19. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Number and Quantity (9 – 12) The Real Number System Quantities The Complex Number System Vector and Matrix Quantities © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

20. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Expressions and Equations (6 – 8) Treat expressions as objects to reason about (not as instructions to compute an answer) Transform expressions using properties of operations Solve linear equations Use variables and equations as techniques to solve word problems Next Stream © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

21. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Operations and Algebraic Thinking (K-5) Concrete uses and meanings of the basic operations (word problems) Mathematical meaning and formal properties of the basic operations Prepare for later work with expressions and equations in middle school © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

22. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Geometry (K – 8) Ascend through progressively higher levels of logical reasoning about shapes Reason spatially with shapes, leading to logical reasoning about transformations Connect geometry to number, operations, and measurement via notion of partitioning © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

23. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Geometry (9 – 12) Congruence Similarity, Right Triangles, and Trigonometry Circles Expressing Geometric Properties with Equations Geometric Measurement and Dimension Modeling with Geometry © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

24. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Number and Operations Fractions (3 – 5) Enlarge concept of number beyond whole numbers, to include fractions Use understanding of the four operations to extend arithmetic to fractions Solve word problems related to the equation ax = b (a and b fractions) Next Stream © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

25. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Ratios and Proportional Relationships (6 – 8) Extend work on multiplication and division; consolidate multiplicative reasoning Lay groundwork for linear functions in Grade 8 by studying quantities that vary together Solve a wide variety of problems with ratios, rates, percents © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

26. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Functions (8) Extend and formalize understanding of quantitative relationships from Grades 3-7 Lay groundwork for more extensive work with functions in High School © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

27. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Functions (9 – 12) Interpreting Functions Building Functions Linear Quadratic and Exponential Models Trigonometric Functions © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

28. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Measurement and Data (K – 5) Emphasize the common nature of all measurement as iterating by a unit Build understanding of linear spacing of numbers and support learning of the number line Develop geometric measures Work with data to prepare for Statistics and Probability in middle school Next Stream © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

29. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Statistics and Probability (6 – 8) Introduce concepts of central tendency, variability, and distribution Connect randomness with statistical inference Lay foundations for High School Statistics and Probability © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

30. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Statistics and Probability (9 - 12) Interpreting Categorical and Quantitative Data Making Inferences and Justifying Conclusions Conditional Probability and the Rules of Probability Using Probability to Make Decisions © Copyright 2011 Institute for Mathematics and Education Next Stream Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.

31. Modeling K 1 2 3 4 5 6 7 8 9 10 11 12 The Common Core State Standards in Mathematics Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Modeling (9 – 12) Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol ( ★ ). Map © Copyright 2011 Institute for Mathematics and Education Click on any red domain for more details. Click on the upper left corner for the next stream through the standards.